Nearly three years after its landmark ruling upholding a race-based admissions plan at the University of Michigan Law School, the US Supreme Court has agreed to consider to what extent race may be used to balance white and nonwhite enrollment in public schools.

On Monday, the high court agreed to examine cases involving two school districts attempting to maintain racially integrated schools.

The second is a school district in Louisville, Ky., that set broad guidelines that the black student population of any particular school should range between 15 percent and 50 percent.

Both cases will be closely watched for indications of how the new lineup of justices - including the replacement of Justice Sandra Day O'Connor with Justice Samuel Alito - may shift the court's jurisprudence on the constitutionality of affirmative action plans.

Justice O'Connor provided the key swing vote and authored the landmark 5-4 decision upholding the University of Michigan Law School's admissions plan. The majority opinion recognized that diversity in education can be a compelling interest, justifying the use of race in the student selection process.

The decision drew sharp dissents from four members of the court's conservative wing, who wrote that the Michigan plan violated the Constitution's equal protection mandate by relying too heavily on race as a factor in the admissions process.

At issue in both the Seattle and Louisville cases is how the high court's 2003 Michigan Law School decision should be applied in public school districts seeking to achieve diversity.

The Kentucky plan relies in large part on school administrators drawing boundaries for each school that extend into both white and black neighborhoods. School enrollment is then determined in part by randomly selecting students from an integrated pool of prospective students.

As an additional boost to integration efforts, school officials tracked prospective students by classifying each as "black male," "black female," "white male," or "white female." This aspect of the Kentucky plan was struck down by a federal judge as an impermissible use of race and gender for public school admissions.

The judge and an appeals court panel upheld the rest of the Kentucky plan.

A parent filed an appeal to the Supreme Court claiming that school officials violated the constitutional guarantee of equal protection when they refused to allow her son to attend his neighborhood school and later refused to allow him to transfer to another elementary school because there were no more slots available at that school for white students.

The judge said the boy was not unduly harmed by the denial of the transfer under the racial guidelines. Because the school district maintains equal and integrated schools, prospective students enjoy no particular benefit by attending one school rather than another, the judge ruled.

But the district's schools are not all equal, argues Teddy Gordon, a Louisville lawyer who represents the mother of the student denied admission to his neighborhood school. Mr. Gordon says in his brief to the Supreme Court that the school district should be focusing on the quality of neighborhood schools rather than the skin color of children attending them.

A similar debate is under way in Seattle. Its school board plan was designed to counter the impact of racially segregated housing patterns on the city's school system. School officials were concerned that reliance on neighborhood schools would simply mirror the city's segregated housing market and translate into a similarly segregated public school system.

To try to break that cycle, the district adopted its "Open Choice" plan in which parents were permitted to send their children to any school within the city. The school board established "tiebreakers" to help determine enrollment at the most popular high schools in the system.

If a student had a sibling at a particular school, that student would be given priority to attend the same school. But if there were no siblings, the "integration tiebreaker" would kick in. In effect, students who were members of an "oversubscribed" race would be given a lower priority for admission than any students of the desired race.

At high schools in the city's largely white north side, that generally meant that minority students were given preference, while at schools in Seattle's largely minority south side, white students were given preference.

Critics of the plan formed a group called Parents Involved in Community Schools. They sued the school district, saying the plan was an unconstitutional form of racial discrimination.

The school district defended the plan as a justifiable effort to achieve racial diversity in the public school system. The plan was adopted in 1998, but has been suspended since 2002 pending the outcome of the litigation.

A federal judge, the Washington Supreme Court, and the Ninth US Circuit Court of Appeals have all upheld Seattle's Open Choice program.

The state supreme court in a 2003 decision rejected the parents' arguments, saying that a racially diverse school population provides educational benefits for all students.